In-depth exploration of the implications of carrier populations and Fermi energies examines distribution of electrons in energy bands and impurity levels of semiconductors. Also: kinetics of semiconductors containing excess carriers, particularly in terms of trapping, excitation, and recombination. 1962 edition.
Unabridged, corrected and slightly enlarged Dover republication of the edition published by Pergamon Press, New York, 1962 (Vol. 3 in the International Series of Monographs on Semiconductors, edited by Heinz K. Henisch).

Table of Contents for Semiconductor Statistics

Preface to the Dover Edition
Part I.
SEMICONDUCTORS IN THERMAL EQUILIBURIUM
Chapter 1.
BASIC CONCEPTS IN THE ELECTRON THEORY OF SOLIDS
1.1 Classical Theories of Metallic Conduction
1.1.1 Drude's Model
1.1.2 Lorentz's Model
1.2 Quantum Statistics and the Free Electron Theory
1.2.1 p-Space and K-Space. The Density of States
1.2.2 Pauli's Exclusion Principle and Fermi-Dirac Statistics
1.2.3 Degeneracy of an Electron Distribution. Sommerfeld's Model
1.3 The Band Theory of Solids
1.3.1 Schrödinger's Equation-One-electron Functions
1.3.2 The Energy-Wave-Vector Relationship. Brillouin Zones
1.3.3 Filling of Energy Bands-Metals and Insulators
1.3.4 Thermal Excitation in Semiconductors
1.3.5 Validity of the Band Model
1.4 The Effective Mass of Charge Carriers
1.4.1 Phase and Group Velocities
1.4.2 The Reduced Zone
1.4.3 The Effective Mass
1.4.4 The Density of States
1.4.5 Mass Renormalization in Band Theory
1.4.6 Magnetic Sub-bands
1.5 Band Shapes for Some Representative Semiconductors
1.5.1 The Band Structure of Silicon
1.5.2 Germanium
1.5.3 Indium Antimonide
1.6 Some Varieties of Impurity Center (Flaw)
1.6.1 Impurities in Elemental Semiconductors Such as Ge and Si
1.6.2 Donors and Acceptors in Compound Semiconductors
Chapter 2.
THE FERMI LEVEL-ELECTRON DENSITY EQUILIBRIUM
2.1 The Fermi-Dirac Integrals
2.1.1 Equivalence of Formalism for Electron and Hole Populations
2.2 Interrelation of Free Electron Density and Fermi Level
2.2.1 Temperature-independent Electron Density
2.2.2 The Effect of a Magnetic Field
2.3 Intrinsic Semiconductors
2.3.1 Non-degenerate Intrinsic Semiconductors
2.3.2 Degenerate Intrinsic Semiconductors
2.4 The Product nopo and ø for Intrinsic and Extrinsic Situations
2.5 Spatial Fluctuations of Carrier Density
2.5.1 Spatial Fluctuations of the Intrinsic Gap
2.5.2 Spatial Fluctuations of Impurity Density
Chapter 3.
SEMICONDUCTORS DOMINATED BY IMPURITY LEVELS
3.1 Occupancy Factor for Impurity Levels
3.1.1 Impurity Level Spin Degeneracy
3.2 Semiconductors Controlled by a Single Monovalent Donor Species
3.2.1 Temperature Dependence of no and ø for a Set of Simple Uncompensated Donors
3.2.2 The Realistic Case-Partly Compensated Impurities
3.2.3 The Influence of Excited States
3.2.4 Impurity Gound State Split in the Crystal Field
3.2.5 Impurity States Split by Anisotropic Elastic Strain
3.2.6 Effect of a Magnetic Field on Impurity States
3.2.7 Some Comments in Summary
3.3 Semiconductors Dominated by Several Localized L
3.3.1 Several Independent Types of Monovalent Donor
3.3.2 Electron Distribution Over a Set of Multivalent Flaws
3.3.3 Amphoteric Impurities
3.4 The Influence of Lattice Defects
3.4.1 Non-stoichiometric Compunds
3.4.2 Irradiation Effects
3.5 Impurity Bands and the Behavior of an Impurity Metal
3.5.1 Weak Impurity Metals
3.5.2 Strong Impurity Metals
3.5.3 Occupancy of Weakly Interacting Impurities
Part II.
SEMICONDUCTORS CONTAINING EXCESS CARRIERS
Chapter 4
FACTORS AFFECTING CARRIER TRANSITION RATES
4.1 Reciprocity of Transition Probabilities
4.1.1 The Principle of Detailed Balance
4.1.2 Electrochemical Potentials and Mean Capture Coefficients
4.2 The Continuity Equations
4.2.1 Some Definitions of Carrier Lifetime
4.3 Band-to-Band and Band-to-Flaw Transitions
4.3.1 Transitions Across the Intrinsic Gap
4.3.2 Transitions to a Localized State (Flaw)
4.3.3 Relative Importance of Recombination Processes
Chapter 5
RADIATIVE AND RADIATIONLESS RECOMBINATION
5.1 The Physics of The Two Processes
5.1.1 Radiative Recombination
5.1.2 Radiationless (Multiphonon) Recombination
5.2 Behavior of the Radiative Lifetime
5.2.1 Equivalence of All Definitions of Lifetime
5.2.2 Variation of Lifetime with Doping and Modulation
5.2.3 The Dependence on Excess Generation Rate
5.2.4 Transient Decay
5.2.5 Variation with Temperature
Chapter 6
BAND-TO-BAND AUGER RECOMBINATION
6.1 Electron-Electron and Hole-Hole Collisions
6.1.1 The Model of Beattie and Landsberg
6.1.2 Net Recombination Rate in Non-equilibrium
6.2 Behavior of the Auger Lifetime when mc< mv
6.2.1 Dependence on Doping and Modulation
6.2.2 The Variation with Generation Rate
6.2.3 Transient Decay
6.2.4 Lifetime-Temperature Relationship
Chapter 7
FREE CARRIER CAPTURE BY FLAWS
7.1 Flaw Capture Mechanisms
7.7.1 Radiative Recombination
7.7.2 Phonon Recombination
7.7.3 Auger Recombination
7.7.4 Relative Probability of the Various Processes
7.2 Behavior of the Extrinsic Lifetime
7.2.1 For Phonon-aided Recombination
7.2.2 For Auger Recombination
7.3 Interaction with Both Bands
Chapter 8
RECOMBINATION THROUGH A SET OF MONOVLENT FLAWS
8.1 The Two Continuity Equations
8.1.1 Capture Cross-sections and Capture Coefficients
8.1.2 Balance Between Generation and Recombination
8.1.3 Adoption of a Dimensionless Notation
8.1.4 Steady State and Transient Decay Equa
8.2 The Criteria of Trapping
8.2.1 Class I and Class II Situations
8.2.2 Electron and Hole Trapping
8.2.3 The Excess Carrier Ratio
8.3 Lifetime for a Small Flaw Density (The S-R Model)
8.3.1 Small-modulation Lifetime
8.3.2 Variation of Lifetime with Modulation
8.3.3 Variation of Excess Density with Steady State Excitation Rate
8.3.4 Transient Decay
8.4 Steady State Conditions for Arbitrary Flaw Density
8.4.1 Small-modulation Lifetime
8.4.2 Finite Modulation
8.5 Transient Decay for Arbitrary Flaw Density
8.5.1 The Initial Stages of Decay
8.5.2 The Final Stages of Decay
8.5.3 The Course of Class I Decay
8.5.4 The Course of Class II Decay
Chapter 9
MORE COMPLICATED EXAMPLES OF FLAW RECOMBINATION
9.1 Multivalent Flaws
9.2 More Than One Kind of Flaw
9.3 The Haynes-Hornbeck Trapping Model
9.3.1 Flaws Which Do Not Capture Holes
9.3.2 Small-modulation Decay
9.3.3 Finite Modulation Trapping Solution
9.3.4 Solution When There is some Hole Capture
9.4 Recombination and Traping at Dislocations
Chapter 10
SPATIAL DISTRIBUTION OF EXCESS CARRIERS
10.1 Approach to the Space-dependent Problem
10.1.1 The Continuity Equations
10.1.2 Assumption of a Constant Lifetime
10.2 Situations Involving Junctions and Contacts
10.2.1 Inhomogeneous Semiconductors
10.2.2 Contact Effects
10.3 Residual Spatial Influences in Homogenous Samples
10.3.1 Surface Recombination
10.3.2 Spatial Distribution of Generation
10.4 Lifetime in Filaments
10.4.1 Homogeneous Equation. Decay Modes
10.4.2 The Amplitudes of Decay Modes
10.4.3 Inhomogeneous Equation. Green's Function Method
APPENDIXES
Appendix A.
THE FERMI-DIRAC DISTRIBUTION LAW
Appendix B.
TABLES OF THE FERMI-DIRAC INTEGRALS
Appendix C.
SOME APPLICATIONS AND PROPERTIES OF THE FERMI-DIRAC INTEGRALS
C.1. Fermi-Dirac Integrals and Transport Properties
C.2. Fermi-Dirac Integrals for Non-standard Bands
C.3. "Analytic Properties of the Fermi Integrals, and Asymptotic Expansions for Non-degenerate and Degenerate Cases"
REFERENCES
INDEX

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